I get stuck at the integration step(Wondering)

use the method of separation of variables to find the solution of the differential equation:

dy/dx=sqrt(2y-y^2)/x+1 , y(0)=1

Printable View

- May 4th 2009, 04:24 AMRaidanSeparation of variables..
**I get stuck at the integration step(Wondering)**

use the method of separation of variables to find the solution of the differential equation:

dy/dx=sqrt(2y-y^2)/x+1 , y(0)=1 - May 4th 2009, 04:44 AMJester
- May 4th 2009, 06:30 AMRaidan
**could someone help me to solve this question?(Bow)** - May 4th 2009, 06:36 AMe^(i*pi)
Danny pointed it out:

u = y-1 so du = dy

Therefore your equation becomes

$\displaystyle \int{\frac{du}{\sqrt{1-u^2}}} = \int{\frac{dx}{x+1}}$

The left side is a standard integral and is equal to $\displaystyle arcsin(u) +A $

wikipedia link (and don't forget to put y-1 wherever u appears)

For the right side recall that $\displaystyle \int{\frac{f'(x)}{f(x)}} = ln|f(x)| + B$

Where A and B are constants and so C = B-A which is also a constant (your constant of integration)